Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

Coma measurement of projection optics in lithographic tools based on relative image displacements at multiple illumination settings

In this paper, we propose a novel method for measuring the coma aberrations of lithographic projection optics based on relative image displacements at multiple illumination settings. The measurement accuracy of coma can be improved because the phase-shifting gratings are more sensitive to the aberrations than the binary gratings used in the TAMIS technique, and the impact of distortion on displacements of aerial image can be eliminated when the relative image displacements are measured. The PROLITH simulation results show that, the measurement accuracy of coma increases by more than 25% under conventional illumination, and the measurement accuracy of primary coma increases by more than 20% under annular illumination, compared with the TAMIS technique. (c) 2007 Optical Society of America.

单纵模相移DFB掺Yb3+光纤激光器运行特性的研究

对我们所制作的λ/4相移DFB掺Yb3+光纤激光器的运行特性进行了研究。研究表明：光纤端面菲涅尔反射会破坏激光器的单纵模运行,因此为获得稳定的羊纵模运行须使用隔离器或甘油清除光纤端面菲涅尔反射；机械扰动则会使沿光纤传输的单偏振激光的偏振面发生变化；温度的涨落则会引起激光输出功率的不稳定涨落。所研制à/4相移DFB单纵模、单偏振激光器具有如下特性：阈值为38mW,当泵浦功率为140 mW时,获得了25mW的1053 nm单 纵模、羊偏振激光.偏振消光比约30 dB,单纵模激光功率涨落小于2%,边模抑制比约6

基于光纤环形镜的全光脉冲整形器

提出了一种基于光纤环形镜的全光脉冲整形器。该全光脉冲整形器利用波分复用器将控制光脉冲引入光纤环形镜中，控制光脉冲由于交叉相位调制在信号光上产生了非线性附加相移。信号光在耦合器中发生干涉，经过整形的信号光脉冲从脉冲整形器的出射端出射，信号脉冲的波形由非线性附加相移的波形决定。实验中．利用对控制脉冲光谱整形和啁啾展宽的方法来对控制脉冲进行时间脉冲的整形，该全光脉冲整形器实现了对单纵模激光的脉冲整形，同时实现了飞秒脉冲和单纵模整形脉冲的精确同步。在理论上数值计算了该全光脉冲整形器的输出特性，理论计算结果和实验结

Stable single frequency and single polarization DFB fiber lasers operated at 1053 nm

Stable single-frequency and single-polarization distributed-feedback (DFB) fiber laser was realized by giving a pressure on the phase shift region of the fiber grating. The output wavelength of the DFB fiber laser is 1053 nm. When the pump power of 980 nm laser diode is 100 and 254 mW, the output power can reach 8.3 and 37.1 mW and the polarization extinction ratio was 26 and 20 dB, respectively. After chopped by Acousto-optic modulator (0.3 Hz), the pulse peak value variance is 4.65%(peak to peak) and 1.098% (RMS) for 31 min. (C) 2006 Elsevier Ltd. All rights reserved.

Split-aperture laser pulse compressor design tolerant to alignment and line-density differences

We introduce a four-pass laser pulse compressor design based on two grating apertures with two gratings per aperture that is tolerant to some alignment errors and, importantly, to grating-to-grating period variations. Each half-beam samples each grating in a diamond-shaped compressor that is symmetric about a central bisecting plane. For any given grating, the two half-beams impinge on opposite sides of its surface normal. It is shown that the two split beams have no pointing difference from paired gratings with different periods. Furthermore, no phase shift between half-beams is incurred as long as the planes containing a grating line and the surface normal for each grating of the pair are parallel. For grating pairs satisfying this condition, gratings surfaces need not be on the same plane, as changes in the gap between the two can compensate to bring the beams back in phase. © 2008 Optical Society of America.

基底微缺陷对介质薄膜光学性能影响的理论研究

基于非均匀膜理论提出一种存在微缺陷的介质基底的折射率分层模型，将基底依次分为表面层、亚表面层和体材料层，其中表面层和亚面层分别等效为折射率服从统计分布的非均匀膜，将它们分别再次细分为N1和N2个子层，每一子层均视为均匀介质膜．应用光学薄膜特征矩阵法对其进行理论分析，并对单层介质膜的光学性能进行数值计算．研究结果表明：基底的表面和亚表面微缺陷改变了薄膜和基底的等效折射率，导致了准Brewster角和组合反射率与理想情形的偏离．同时这些微缺陷也改变了光在薄膜和基底中的传播特性，因此反射相移和相位差均偏离理想情

Theoretical analysis of optical properties of dielectric coatings dependence on substrate subsurface defects

A model for refractive index of stratified dielectric substrate was put forward according to theories of inhomogeneous coatings. The substrate was divided into surface layer, subsurface layer and bulk layer along the normal direction of its surface. Both the surface layer (separated into N-1 sublayers of uniform thickness) and subsurface layer (separated into N-2 sublayers of uniform thickness), whose refractive indices have different statistical distributions, are equivalent to inhomogeneous coatings, respectively. And theoretical deduction was carried Out by employing characteristic matrix method of optical coatings. An example of mathematical calculation for optical properties of dielectric coatings had been presented. The computing results indicate that substrate subsurface defects can bring about additional bulk scattering and change propagation characteristic in thin film and Substrate. Therefore, reflectance, reflective phase shift and phase difference of an assembly of coatings and substrate deviate from ideal conditions. The model will provide some beneficial theory directions for improving optical properties of dielectric coatings via substrate surface modification. (c) 2005 Elsevier B.V. All rights reserved.

Theoretical analysis of influence of substrate microdefects on polarized light properties of dielectric coatings

A model for refractive index of stratified dielectric substrate was presented according to inhomogeneous coatings theories. The substrate was divided into surface layer, subsurface layer and bulk layer along the normal direction of its surface. The former two layers were equivalent to inhomogeneous coatings. Theoretical deduction was executed by employing the characteristic matrix method of optical coatings, and one mathematical calculation example was presented. The results indicate that reflectance, reflective phase shift and phase difference of polarized light deviate from ideal conditions. It shows that substrate microdefects can induce volume scattering and change propagation characteristic of light both in coatings and substrate. (c) 2005 Elsevier GmbH. All rights reserved.

光学薄膜中界面层和表面吸附层对相位延迟的影响

多层介质反射镜在非正入射的时候，两个不同的偏振态之间会产生不同的相移．根据空气与膜层、膜层之间的实际情况，建立了界面层和表面吸附层模型，并运用它分析相位延迟产生误差的原因．通过优化设计，入射角为54°，在1285～1345nm之间p，s波获得了270±1°的相移，同时也使反射率在99．5％以上．用离子束溅射技术制备相位延迟膜，用分光光度计测试了光谱特性和用椭偏仪测试了相位特性，在相应波段获得了262．4±1．8°的相移，同时也使反射率在99．6％以上．误差的主要来源是离子源工作特性会产生不均匀的过渡层和最

氧碘激光器相位延迟片的制备与性能研究

多层介质反射镜在非正入射的时候，两个不同的偏振态之间会产生不同的相移。利用矩阵法，根据菲涅耳公式和电磁场边界条件，推导出p，s波的相移。通过优化设计．入射角为54°，在1285～1345nm之间p，s波获得了270°±1°的相移，同时也使反射率在99．5％以上。用离子束溅射技术制备相位延迟膜，用分光光度计测试了光谱特性和用椭偏仪测试了相位特性，在相应波段获得了262．4°±1．8°的相移，同时也使反射率在99．6％以上。误差的主要来源是离子源工作特性会产生不均匀的过渡层和最外层会吸收一些水气、灰尘等也产生

反射式相位延迟器的性能研究

多层介质反射镜在非正入射的时候，两个不同的偏振态之间会产生不同的相移。通过优化设计，入射角为45°，在1285～1345nm之间p，s波获得了270°±0．15°的相移和99．5％以上的反射率。对使用的膜系进行了每层光学厚度的误差分析。用离子柬溅射技术制备相位延迟膜，在大气中对样品进行不同温度的退火，用分光光度计测试了光谱特性和用椭偏仪测试了相位特性。结果表明，未退火的样品在相应波段获得了267．5°±0．5°的相移和99．6％以上的反射率；根据拟合分析，最外层的误差和折射率与设计值的偏差是发生相移偏小的

Interações competitivas entre Epizoanthus gabrieli Carlgreen, 1951 (Ordem Zoanthidea) e corais na Baía de Todos os Santos e suas implicações para a comunidade recifal.

Alguns recifes de coral da Baía de Todos os Santos passaram a ser dominado pelo zoantídeo Epizoanthus gabrieli em 2003. Fenômeno resultante da degradação dos recife de coral que atinge 20% desses ecossistemas e ameaça outros 35% no mundo. Apesar de sua importância, apenas a mudança na comunidade para o domínio de macroalgas foi suficientemente estudado. Assim, torna-se urgente estudos sobres alterações envolvendo a dominância de outros organismos. Estes fornecem subsídios para produção de modelos funcionais que podem ajudar na tomada de decisão para o manejo destes ecossistemas tanto na prevenção destas alterações quanto na recuperação de suas comunidades. Os objetivos deste trabalho são (i) verificar se este fenômeno constitui uma mudança de fase, a partir da redução da abundância de corais e persistência da alta cobertura de E. gabrieli por pelo menos cinco anos, (ii) avaliar os efeitos da competição entre este zoantídeo e corais adultos e recrutas com experimentos manipulativos e (iii) investigar os efeitos desta dominância na assembleia de peixes recifais. Os resultados confirmaram a existência de uma mudança de fase, sugerindo que a abundância de E. gabrieli aumentou em 2003 ou antes e que até 2007 houve uma redução da cobertura de coral, condição que se mantêm pelo menos até 2013. As três espécies de corais testadas mostram-se muito sensíveis ao contato com E. gabrieli, com necrose em 78% das colônias e ocupação do esqueleto dos corais em 35% dos casos em um período de 118 dias. Além disso, um modelo feito a partir dos dados de proporção de colônias de corais em contato com este zoantídeo e a cobertura de E. gabrieli sugere que quando o zoantídeo atinge 6% de cobertura, 50% das colônias de corais entram em contato com o mesmo. Estes dados são fortes evidências de que a redução da cobertura de coral observada entre 2003 e 2007 foi causada por competição entre estes organismos. Não foi observado efeito negativo no recrutamento do coral em substrato artificial livre em recifes dominados por E. gabrieli, nem nas proximidades das suas colônias. Isso sugere que uma suposta redução da cobertura deste zoantídeo deve ser acompanhada pelo aumento da taxa de recrutamento de corais e que a competição com a inibição do recrutamento não suporta um efeito de histerese. Foi constatado que esta mudança de fase reduz a riqueza de espécies de peixes recifais, apresentando dez espécies a menos que os recifes normais, e que favorecem os invertívoros moveis em detrimento dos carnívoros e invertívoros sésseis. Contudo não se observou diferença na abundância de peixes.

Bias-dependent recovery time of all-optical resonant nonlinearity in InGaAsP/InGaAsP MQW waveguide

We have investigated a resonant refractive nonlinearity in a semiconductor waveguide by measuring intensity dependent phase shifts and bias-dependent recovery times. The measurements were performed on an optimized 750-μm-long AR coated buried heterostructure MQW p-i-n waveguide with a bandedge at 1.48 μm. Figure 1 shows the experimental arrangement. The mode-locked color center laser was tuned to 50 meV beyond the bandedge and 8 ps pulses with peak incident power up to 57 W were coupled into the waveguide. Some residual bandtail absorption remains at this wavelength and this is sufficient to cause carriers to be photogenerated and these give rise to a refractive nonlinearity, predominantly by plasma and bandfilling effects. A Fabry-Perot interferometer is used to measure the spectrum of the light which exits the waveguide. The nonlinearity within the guide causes self phase modulation (SPM) of the light and a study of the spectrum allows information to be recovered on the magnitude and recovery time of the nonlinear phase shift with a reasonable degree of accuracy. SPM spectra were recorded for a variety of pulse energies coupled into he unbiased waveguide. Figure 2 shows the resultant phase shift measured from the SPM spectra as a function of pulse energy. The relationship is a linear one, indicating that no saturation of the nonlinearity occurs for coupled pulse energies up to 230 pJ. A π phase shift, the minimum necessary for an all-optical switch, is obtained for a coupled pulse energy of 57 pJ while the maximum phase shift, 4 π, was measured for 230 pJ. The SPM spectra were highly asymmetric with pulse energy shifted to higher frequencies. Such spectra are characteristic of a slow, negative nonlinearity. This relatively slow speed is expected for the unbiased guide as the recovery time will be of the order of the recombination time of the photogenerated electrons, about 1 ns for InGaAsP material. In order to reduce the recovery time of the nonlinearity, it is necessary to remove the photogenerated carriers from the waveguide by a process other than recombination. One such technique is to apply a reverse bias to the waveguide in order to sweep the carriers out. Figure 3 shows the effect on the recovery time of the nonlinearity of applying reverse bias to the waveguide for 230 pJ coupled power. The recovery time was reduced from one much longer than the length of the pulse, estimated to be about 1 ns, at zero bias to 18 ± 3 ps for a bias voltage greater than -4 V. This compares with a value of 24 ps obtained in a bulk waveguide.

Efficient registration of nonrigid 3-D bodies

We present a novel method to perform an accurate registration of 3-D nonrigid bodies by using phase-shift properties of the dual-tree complex wavelet transform (DT-CWT). Since the phases of DT-\BBCWT coefficients change approximately linearly with the amount of feature displacement in the spatial domain, motion can be estimated using the phase information from these coefficients. The motion estimation is performed iteratively: first by using coarser level complex coefficients to determine large motion components and then by employing finer level coefficients to refine the motion field. We use a parametric affine model to describe the motion, where the affine parameters are found locally by substituting into an optical flow model and by solving the resulting overdetermined set of equations. From the estimated affine parameters, the motion field between the sensed and the reference data sets can be generated, and the sensed data set then can be shifted and interpolated spatially to align with the reference data set. © 2011 IEEE.